The present invention relates to a method of estimating tire performance, a method of fluid simulation, a method of designing a pneumatic tire, a method of designing a vulcanizing mold for a tire, a method of make a vulcanizing mold for a tire, a method of manufacturing a pneumatic tire, an optimization analyzer, a recording medium with a tire-performance estimation program recorded thereon, and a recording medium with a tire optimization analysis program recorded thereon. Specifically, the present invention relates to a tire-performance estimating method for estimating the performance of a pneumatic tire used in an automobile or the like, particularly the tire performance in the presence of a fluid such as the drainage performance, in-snow performance, and noise performance, a fluid simulation method for simulating the flow of a fluid around a tire, a method of designing a pneumatic tire, a method of designing a vulcanizing mold for a tire for designing a vulcanizing mold for manufacturing a tire, a method of manufacturing a pneumatic tire, and a recording medium with a tire-performance estimation program recorded thereon, or a method of designing a pneumatic tire which makes it possible to efficiently and easily design and develop the structure, shape and the like of a tire for attaining the single-purpose performance, mutually incompatible performances and the like of the tire, and which makes it possible to determine an optimal structure and shape of the tire and design a tire exhibiting high cost performance, as well as an optimization analyzer and a recording medium with a tire optimization analysis program recorded thereon.
Conventionally, in the development of a pneumatic tire, tire performance is obtained by conducting performance tests by actually designing and fabricating a tire and mounting it on an automobile, and a procedure has been adopted in which the development is redone starting from the design and fabrication unless the results of the performance tests are satisfactory. In recent years, owing to the development of numerical analysis techniques such as the finite element method and the computer environment, it has become possible to estimate by computers such as the state of inflation of the tire with internal pressure and the state of load at the time the tire is not rolling, and it has become possible to estimate a number of performances from this estimation. However, it has hitherto been impossible to compute those tire performances that are determined by the behavior of a fluid, such as the drainage performance, in-snow performance, and noise performance. For this reason, the present situation is such that it is impossible to conduct the estimation of tire performance and efficiently perform tire development.
A technical document is known in which an attempt was made to analyze the drainage performance, particularly hydroplaning, of a tire with respect to a smooth tire (grooveless tire) and a tire provided with only circumferential grooves (xe2x80x9cTire Science and Technology, TSTCA, Vol. 25, No. 4, October-December, 1997, pp. 265-287xe2x80x9d).
However, in this conventional technical document, analysis is attempted with respect to only the smooth (i.e., grooveless) tire and the tire provided with only circumferential grooves, and no reference is given to tires with patterns having inclined grooves intersecting the circumferential direction of the tire, which largely contribute to the drainage performance in actual tires, nor to how the fluid during the ground contacting and rolling of the tire can be brought close to a flowing state and how transient analysis can be made possible. Namely, no consideration is given to the analysis in which an actual environment is assumed with respect to an actual tire.
In view of the above-described facts, an object of the invention is to obtain a method of estimating tire performance which is capable of facilitating the estimation of the performance of an actually used tire in the presence of a fluid, such as the drainage performance, in-snow performance, and noise performance, a method of fluid simulation, a method of designing a pneumatic tire which renders tire development efficient and is capable of obtaining a tire exhibiting excellent performance, a method of designing a vulcanizing mold for a tire, a method of making a vulcanizing mold for a tire, a method of manufacturing a pneumatic tire, and a recording medium with a tire-performance estimation program recorded thereon.
The design of tires has been based on experiential rules obtained through repeated numerical experiments using experiments and computers. For this reason, the number of trial manufactures and tests required for development has been enormously large, resulting in increased development cost and making it impossible to readily reduce a development period.
The design of a tire includes the design of the structure, shape, and pattern of the tire. To design the structure, shape, and pattern of the tire is to determine, for example, the structure, shape, pattern, and manufacturing conditions for obtaining the targeted tire performance. This tire performance is a result of evaluation of physical quantities determined by computations and experiments as well as actual-vehicle feeling. The conventional methods of designing a tire including, for example, the design of the structure, shape, and pattern of the tire have been based on experiential rules obtained on a trial-and-error basis through repeated numerical experiments using experiments and computers. For this reason, the number of trial manufactures and tests required for development has been enormously large, resulting in increased development cost and making it impossible to readily reduce the development period.
As means for overcoming these problems, techniques for obtaining optimal solutions have been proposed such as optimization methods using mathematical programming and genetic algorithms. As a technique relating to this mathematical programming, the present applicant already proposed a designing method disclosed in already-filed International Publication No. WO 94/16877.
Obtaining an optimal solution is likened to mountain-climbing. At this time, since the altitude of the mountain is related to the performance, the optimal solution corresponds to the peak of the mountain. In a case where the objective function is simple, its design space (i.e., the shape of the mountain) has the shape of a mountain with one peak, so that the optimal solution can be obtained by an optimization technique based on mathematical programming.
In the development of a pneumatic tire, the tire performance to be considered is obtained by conducting performance tests by actually designing and fabricating a tire and mounting it on an automobile, and a procedure has been adopted in which the development is redone starting from the design and fabrication unless the results of the performance tests are satisfactory. In recent years, due to the development of numerical analysis techniques such as the finite element method and the computer environment, it has become possible to estimate by the computer such as the state of inflation of the tire with internal pressure and the state of load when the tire is not rolling, and it has become possible to estimate a number of performances from this estimation. However, it has been impossible to compute those tire performances that are determined by the behavior of a fluid, such as the drainage performance, in-snow performance, and noise performance. For this reason, the present situation is such that it has been impossible to conduct the estimation of tire performance and efficiently perform tire development.
A technical document is known in which an attempt was made to analyze the drainage performance, particularly hydroplaning, of a tire with respect to a smooth tire (grooveless tire) and a tire provided with only circumferential grooves (xe2x80x9cTire Science and Technology, TSTCA, Vol. 25, No. 4, October-December, 1997, pp. 265-287xe2x80x9d).
However, in such conventional consideration of the drainage performance of the tire, an attempt is made in the analysis with respect to only the smooth (i.e., grooveless) tire and the tire provided with only circumferential grooves, but no reference is given to tires with patterns having inclined grooves intersecting the circumferential direction of the tire, which large contribute to the drainage performance in actual tires, nor to how the fluid during the ground contacting and rolling of the tire can be brought close to a flowing state and how transient analysis can be made possible. Namely, no consideration is given to the analysis in which an actual environment is assumed with respect to an actual tire.
In addition, in the design and development of a tire, a targeted value is set for a certain performance, and if this targeted value is cleared, the design and development of the tire are considered to be completed for the present, and have not been such that the best performance is obtained with the given resources. In addition, the tire design and tire performance tests are conducted independently, and the development of the tire is effected by repeating trial manufacture and testing on a trial-and-error basis, so that the development of the tire has been very inefficient.
In view of the above-described facts, another object of the invention is to obtain a method of designing a pneumatic tire which is capable of the design and development of a tire with high efficiency while estimating the performance of an actually used tire in the presence of a fluid, such as the drainage performance, in-snow performance, and noise performance, as well as an optimization analyzer and a recording medium with a tire optimization analysis program recorded thereon.
To attain the above objects, in the present invention, the performance of an actually used tire in the presence of a fluid, such as the drainage performance, in-snow performance, and noise performance, is estimated. In particular, the fluid during the ground contacting and rolling of the tire is brought close to a flowing state, and transient analysis is made possible. In addition, the development of the tire is made efficient, and the provision of the tire having excellent performance is facilitated.
Specifically, the method of estimating tire performance according to claim 1 comprises the steps of: (a) determining a tire model having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and determining a fluid model which is partially or wholly filled with a fluid and which comes into contact with at least a portion of the tire model; (b) executing a deformation calculation of the tire model; (c) executing a fluid calculation of the fluid model; (d) identifying a boundary surface between the tire model after the deformation calculation in step (b) and the fluid model after the fluid calculation in step (c), imparting a boundary condition concerning the identified boundary surface to the tire model and the fluid model, and performing the deformation calculation and the fluid calculation until the fluid model assumes a state of pseudo flow; (e) determining a physical quantity occurring in at least one of the tire model and the fluid model in step (c) or step (d); and (f) estimating the tire performance on the basis of the physical quantity.
In accordance with the invention according to claim 2, in the method of estimating tire performance according to claim 1, in step (a), a road surface model in contact with the fluid model is further determined.
In accordance with the invention according to claim 3, in the method of estimating a tire performance according to claim 1 or 2, in step (b), the deformation calculation is performed repeatedly for only a predetermined time duration.
In accordance with the invention according to claim 4, in the method of estimating a tire performance according to claim 3, the predetermined time duration is 10 msec or less.
In accordance with the invention according to claim 5, in the method of estimating a tire performance according to any one of claims 1 to 4, in step (c), the fluid calculation is performed repeatedly for only a fixed time duration.
In accordance with the invention according to claim 6, in the method of estimating a tire performance according to claim 5, the fixed time duration is 10 msec or less.
In accordance with the invention according to claim 7, in the method of estimating a tire performance according to any one of claims 1 to 6, in step (d), the calculations are performed repeatedly for only a time duration determined in advance.
In accordance with the invention according to claim 8, in the method of estimating a tire performance according to claim 7, the time duration determined in advance is 10 msec or less.
In accordance with the invention according to claim 9, in the method of estimating a tire performance according to any one of claims 1 to 8, in a case where the tire model is rolled, in step (a), the tire model is determined for which the calculation for charging with internal pressure and load calculation is performed, and to which a rotational displacement or a speed or a straightly advancing displacement is imparted.
In accordance with the invention according to claim 10, in the method of estimating a tire performance according to any one of claims 1 to 8, in a case where the tire model is rolled, in step (a), influx and efflux conditions representing that the fluid flows out freely from a top surface of the fluid model and that the fluid does not flow into or flow out of surfaces other than the top surface of the fluid model are imparted to the fluid model.
In accordance with the invention according to claim 11, in the method of estimating a tire performance according to any one of claims 1 to 8, in a case where the tire model is not rolled, in step (a), the tire model is determined for which the deformation calculation for a time of charging with internal pressure is performed, and for which load calculation is performed after the deformation calculation.
In accordance with the invention according to claim 12, in the method of estimating a tire performance according to any one of claims 1 to 8 or claim 11, in a case where the tire model is not rolled, in step (a), influx and efflux conditions representing that the fluid flows into a front surface of the fluid model at an advancing velocity, that the fluid flows out freely from a rear surface of the fluid model and a top surface of the fluid model, and that the fluid does not flow into or flow out of side surfaces of the fluid model and a lower surface of the fluid model are imparted to the fluid model.
In accordance with the invention according to claim 13, in the method of estimating a tire performance according to any one of claims 1 to 12, the tire model has a pattern partially.
In accordance with the invention according to claim 14, in the method of estimating a tire performance according to any one of claims 1 to 13, as for a road surface model, a road surface condition is set by selecting a coefficient of friction xcexc representing at least one of road surface conditions including dry, wet, icy, snowy, and unpaved conditions.
In accordance with the invention according to claim 15, in the method of estimating a tire performance according to any one of claims 1 to 14, in step (d), an interfering portion between the tire model and the fluid model is generated, an interference portion is identified, and the fluid model is divided by fluid elements with a surface of the tire model as a boundary surface.
In accordance with the invention according to claim 16, in the method of estimating a tire performance according to any one of claims 1 to 15, the fluid model contains at least water, at least one of a ground contact area and a ground contact pressure of the tire model is used as the physical quantity, and a wet performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 17, in the method of estimating a tire performance according to any one of claims 1 to 16, the fluid model contains at least water, at least one of a pressure, flow volume, and flow velocity of the fluid model is used as the physical quantity, and a wet performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 18, in the method of estimating a tire performance according to any one of claims 1 to 16, the fluid model contains at least one of water and snow, at least one of a ground contact area, ground contact pressure, and shearing force of the tire model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, and an on-ice and in-snow performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 19, in the method of estimating a tire performance according to any one of claims 1 to 16, the fluid model contains at least one of water and snow, at least one of a pressure, flow volume, and flow velocity of the fluid model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, and an on-ice and in-snow performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 20, in the method of estimating a tire performance according to any one of claims 1 to 16, the fluid model contains at least air, at least one of pressure, flow volume, flow velocity, energy, and energy density of the fluid model is used as the physical quantity, and a noise performance of the tire is estimated as the tire performance.
The fluid simulation in accordance with the invention according to claim 21 comprises the steps of: (a) determining a tire model having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and determining a fluid model which is partially or wholly filled with a fluid and which comes into contact with at least a portion of the tire model; (b) executing a deformation calculation of the tire model; (c) executing a fluid calculation of the fluid model; and (d) identifying a boundary surface between the tire model after the deformation calculation in step (b) and the fluid model after the fluid calculation in step (c), imparting a boundary condition concerning the identified boundary surface to the tire model and the fluid model, and performing the calculations until the fluid model assumes a state of pseudo flow.
The method of designing a pneumatic tire in accordance with the invention according to claim 22 comprises the steps of: (1) determining a plurality of tire models each having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and determining a fluid model which is partially or wholly filled with a fluid and which comes into contact with at least a portion of a tire model; (2) executing a deformation calculation of the tire model; (3) executing a fluid calculation of the fluid model; (4) identifying a boundary surface between the tire models after the deformation calculation in step (2) and the fluid model after the fluid calculation in step (3), imparting a boundary condition concerning the identified boundary surface to the tire models and the fluid model, and performing the calculations until the fluid model assumes a state of pseudo flow; (5) determining a physical quantity occurring in at least one of the tire models and the fluid model in step (3) or step (4); (6) estimating a plurality of tire performances on the basis of the physical quantity; and (7) designing a tire on the basis of a tire model having a tire performance selected from the plurality of tire performances.
The method of designing a vulcanizing mold for a tire in accordance with the invention according to claim 23 comprises the steps of: (xcex1) determining a plurality of tire models having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and determines a fluid model which is partially or wholly filled with a fluid and which comes into contact with at least a portion of the tire model; (xcex2) executing a deformation calculation of each of the tire models; (xcex3) executing a fluid calculation of the fluid model; (xcex4) identifying a boundary surface between the tire models after the deformation calculation in step (xcex2) and the fluid model after the fluid calculation in step (xcex3), imparting a boundary condition concerning the identified boundary surface to the tire model and the fluid model, and performing the calculations until the fluid model assumes a state of pseudo flow; (xcex5) determining a physical quantity occurring in at least one of the tire models and the fluid model in step (xcex3) or step (xcex4); (xcex6) estimating a plurality of tire performances of each of the tire models on the basis of the physical quantity; and (xcex7) designing the vulcanizing mold for the tire on the basis of one of the tire models having the tire performance selected from the plurality of tire performances.
In accordance with the invention according to claim 24, in the method of make a vulcanizing mold for a tire, a vulcanizing mold for a pneumatic tire, designed by the method of designing a vulcanizing mold for a tire according to claim 23, is made.
In accordance with the invention according to claim 25, in the method of manufacturing a pneumatic tire, a vulcanizing mold for a pneumatic tire, designed by the method of designing a vulcanizing mold for a tire according to claim 23, is made, and the pneumatic tire is manufactured by using the vulcanizing mold.
The method of manufacturing a pneumatic tire in the invention in accordance with claim 26 comprises the steps of: (I) determining a plurality of tire models each having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and determining a fluid model which is partially or wholly filled with a fluid and which comes into contact with at least a portion of the tire models; (II) executing a deformation calculation of each of the tire models; (III) executing a fluid calculation of the fluid model; (IV) identifying a boundary surface between each of the tire models after the deformation calculation in step (II) and the fluid model after the fluid calculation in step (III), imparting a boundary condition concerning the identified boundary surface to each of the tire models and the fluid model, and performing the calculations until the fluid model assumes a state of pseudo flow; (V) determining a physical quantity occurring in at least one of the respective tire models and the fluid model for each of the tire models in step (III) or step (IV); (VI) estimating a tire performance of each of the tire models on the basis of the physical quantity; and (VII) manufacturing the tire on the basis of a tire model having a tire performance selected from the plurality of tire performances.
The recording medium with a tire-performance estimation program recorded thereon for estimating a tire performance by a computer in the invention in accordance with claim 27 comprises the steps of: (A) determining a tire model having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and determining a fluid model which is partially or wholly filled with a fluid and which comes into contact with at least a portion of the tire model; (B) executing a deformation calculation of the tire model; (C) executing a fluid calculation of the fluid model; and (D) identifying a boundary surface between the tire model after the deformation calculation in step (B) and the fluid model after the fluid calculation in step (C), imparting a boundary condition concerning the identified boundary surface to the tire model and the fluid model, and performing the calculations until the fluid model assumes a state of pseudo flow.
In the method of estimating tire performance in accordance with the present invention, first, a draft design of the tire is incorporated into a model in numerical analysis so as to estimate the performance of a tire to be evaluated (such as the change of the shape, structure, materials, and pattern of the tire). Further, modeling of a fluid and a road surface concerning the targeted performance is performed to construct a fluid model and a road surface model (numerical analysis models), numerical analysis which simultaneously takes into consideration the tire, the fluid, and the road surface is carried out, and the targeted performance is numerically estimated. The acceptability of the draft design of the tire is determined from the result of this estimation, and if the result is favorable, the draft design is adopted, or a tire of this draft design is manufactured, and the performance evaluation is conducted. If these results up to this stage are satisfactory, the draft design is adopted. If the estimate d performance (or actually measured performance) based on the draft design is unsatisfactory, a part or the whole of the draft design is corrected, and the procedures are carried out again starting with the construction of the numerical analysis models. If these procedures are used, the number of times the tire is manufactured and the performance is evaluated can be minimized, so that the development of the tire can be made efficient.
Accordingly, to undertake the development of the tire based on the estimation of performance, numerical analysis models for the tire performance estimation which is efficient and highly accurate are essential. Accordingly, in the present invention, to estimate the tire performance, in step (a), a tire model having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, as well as a fluid model which is filled with a fluid and comes into contact with at least a portion of the tire model, are determined. Incidentally, a road surface model may be further determined. In step (b), deformation calculation of the tire model is executed and, in step (c), fluid calculation of the fluid model is executed. In step (d), a boundary surface between the tire model after the deformation calculation in step (b) and the fluid model after the fluid calculation in step (c) is recognized, a boundary condition concerning the recognized boundary surface is imparted to the tire model and the fluid model, and the calculation is performed until the fluid model assumes a state of pseudo flow. In step (e), a physical quantity occurring in at least one of the tire model and the fluid model in step (c) or step (d) is determined and, in step (f), the tire performance is estimated on the basis of the physical quantity.
In the deformation calculation of the tire model in step (b), deformation calculation at a time when deformation is imparted by at least one of ground contacting and rolling can be executed. In this case, at least one of the ground contacting and rolling may be set as the input.
In addition, when a boundary condition concerning the recognized boundary surface is imparted to the tire model and the fluid model, the fluid model may be determined in such a manner that the fluid is present on the road surface model side relative to the boundary surface.
It should be noted that, in at least one of the deformation calculation of the tire model and fluid calculation, repeated calculation may be performed. In the deformation calculation of the tire model, 10 msec or less may be adopted as the elapsed time of the predetermined time duration during which the repeated calculation is performed. Preferably, it is possible to adopt 1 msec or less, more preferably 1xcexcxc2x7sec or less. In addition, in the fluid calculation, 10 msec or less may be adopted as the elapsed time of the fixed time duration during which the repeated calculation is performed. Preferably, it is possible to adopt 1 msec or less, more preferably 1xcexcxc2x7sec or less. If this elapsed time is too long, the fluid in the fluid model fails t o assume a state of pseudo flow conforming to the behavior of the tire, and the accuracy as a numerical model deteriorates. For this reason, it is necessary to adopt an appropriate value as the elapsed time.
In addition, repeated calculation may be performed also in the calculation until the fluid model assumes the state of pseudo flow. In this calculation, 10 msec or less may be adopted as the elapsed time of the predetermined time duration during which the repeated calculation is performed. Preferably, it is possible to adopt 1 msec or less, more preferably 1xcexcxc2x7sec or less.
The aforementioned tire model may have a pattern partially. Further, as for the road surface model, an actual road surface condition can be reproduced by selecting a coefficient of friction xcexc representing a road surface condition among the dry, wet, icy, snowy, unpaved and other conditions depending on the road surface condition.
When the boundary condition is imparted, it is important that the fluid model recognize the surface of the tire model as the boundary surface of the fluid. However, if the very fine elements making up the fluid model are always made sufficiently small with respect to the tire (particularly pattern) model, and the number of constituent elements of the fluid model hence increases, an increase in the calculation time results, which entails difficulty. Accordingly, it is preferable to prevent an increase in the calculation time by making the very fine elements making up the fluid model large to a certain measure. At the same time, it is preferable to produce (overlap) an interfering portion between the tire model and the fluid model, recognize the interference portion, and divide the fluid model with the surface of the tire model as a boundary surface, so as to allow the boundary surface between the tire model and the fluid model to be recognized with high accuracy.
In addition, if the fluid model contains at least water, and the ground contact area or ground contact pressure of the tire model is used as the physical quantity, it is possible to estimate the wet performance of the tire. Further, if the fluid model contains at least water, and the pressure, flow volume, or flow velocity of the fluid model is used as the physical quantity, it is possible to estimate the wet performance of the tire.
Further, if the fluid model contains at least one of water and snow, and at least one of the ground contact area, ground contact pressure, and shearing force of the tire model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, it is possible to estimate the on-ice and in-snow performance of the tire. In addition, if the fluid model contains at least one of water and snow, and at least one of the pressure, flow volume, and flow velocity of the fluid model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, it is possible to estimate the on-ice and in-snow performance of the tire.
Further, if the fluid model contains at least water, and at least one of the pressure, flow volume, flow velocity, energy, and energy density of the fluid model is used as the physical quantity, it is possible to estimate the noise performance of the tire.
Further, in a case where the behavior of the fluid around the tire is simulated, if the following steps are taken which include: (a) determining a tire model having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and a fluid model which is partially or wholly filled with a fluid and comes into contact with at least a portion of the tire model; (b) executing deformation calculation of the tire model; (c) executing fluid calculation of the fluid model; and (d) recognizing a boundary surface between the tire model after the deformation calculation in step (b) and the fluid model after the fluid calculation in step (c), imparting a boundary condition concerning the recognized boundary surface to the tire model and the fluid model, and performing the calculation until the fluid model assumes a state of pseudo flow, then it is possible to evaluate the flow of the fluid around the tire and estimate the smoothness of flow and the occurrence of disturbance, thereby making it possible to contribute to the estimation of tire performance.
In addition, in the case where the tire is designed, if the following steps are taken which include: (1) determining a plurality of tire models each having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and a fluid model which is partially or wholly filled with a fluid and comes into contact with at least a portion of the tire model; (2) executing deformation calculation of the tire model; (3) executing fluid calculation of the fluid model; (4) recognizing a boundary surface between the tire model after the deformation calculation in step (2) and the fluid model after the fluid calculation in step (3), imparting a boundary condition concerning the recognized boundary surface to the tire model and the fluid model, and performing the calculation until the fluid model assumes a state of pseudo flow; (5) determining a physical quantity occurring in at least one of the tire model and the fluid model in step (3) or step (4); (6) estimating the tire performance on the basis of the physical quantity; and (7) designing the tire on the basis of the tire model having the tire performance selected from the plurality of tire performances, then it is possible to evaluate the flow of the fluid around the tire and contribute to the design while estimating the smoothness of flow and the occurrence of disturbance.
In addition, in a case where a vulcanizing mold for a tire for manufacturing a tire is designed, if the following steps are taken which include: (xcex1) determining a tire model having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and a fluid model which is partially or wholly filled with a fluid and comes into contact with at least a portion of the tire model; (xcex2) executing deformation calculation of the tire model; (xcex3) executing fluid calculation of the fluid model; (xcex4) recognizing a boundary surface between the tire model after the deformation calculation in step (xcex2) and the fluid model after the fluid calculation in step (xcex3), imparting a boundary condition concerning the recognized boundary surface to the tire model and the fluid model, and performing the calculation until the fluid model assumes a state of pseudo flow; (xcex5) determining a physical quantity occurring in at least one of the tire model and the fluid model in step (xcex3) or step (xcex4); (xcex6) estimating the tire performance of each of the tire models on the basis of the physical quantity; and (xcex7) designing the vulcanizing mold for a tire on the basis of the tire model having the tire performance selected from the plurality of tire performances, then it is possible to evaluate the flow of the fluid around the tire to be manufactured and contribute to the design of the mold for manufacturing a tire while estimating the smoothness of flow and the occurrence of disturbance.
If the vulcanizing mold for a tire thus designed is made, the manufacture of the tire which is to assume the estimated tire performance is facilitated. In addition, if this vulcanizing mold for a tire is made, and the tire is manufactured by using it, its tire performance substantially agrees with the estimated performance, and it is possible to obtain a tire in which the evaluation of the flow of the fluid, the smoothness of the flow, the occurrence of disturbance, and the like have been taken into consideration.
In addition, in a case where a tire is manufactured, if the following steps are provided which include: (I) determining a plurality of tire models each having a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, and a fluid model which is partially or wholly filled with a fluid and comes into contact with at least a portion of the tire model; (II) executing deformation calculation of each of the tire models; (III) executing fluid calculation of the fluid model; (IV) recognizing a boundary surface between each of the tire models after the deformation calculation in step (II) and the fluid model after the fluid calculation in step (III), imparting a boundary condition concerning the recognized boundary surface to each of the tire models and the fluid model, and performing the calculation until the fluid model assumes a state of pseudo flow; (V) determining a physical quantity occurring in at least one of each of the tire models and the fluid model for each of the tire models in step (III) or step (IV); (VI) estimating the tire performance of each of the tire models on the basis of the physical quantity; and (VII) manufacturing the tire on the basis of the tire model having the tire performance selected from the plurality of tire performances, then the tire performance substantially agrees with the estimated performance, and it is possible to obtain a tire in which the evaluation of the flow of the fluid, the smoothness of the flow, the occurrence of disturbance, and the like have been taken into consideration.
Further, in a case where tire performance is estimated by a computer, if a tire-performance estimation program which includes the following steps is stored in a storage medium and is executed, and if data is collected: (A) determining a tire model having a pattern configuration to which de formation can be imparted by at least one of ground contacting and rolling, and a fluid model which is partially or wholly filled with a fluid and comes into contact with at least a portion of the tire model; (B) executing deformation calculation of the tire model; (C) executing fluid calculation of the fluid model; and (D) recognizing a boundary surface between the tire model after the deformation calculation in step (B) and the fluid model after the fluid calculation in step (C), imparting a boundary condition concerning the recognized boundary surface to the tire model and the fluid model, and performing the calculation until the fluid model assumes a state of pseudo flow, then it is possible to make a comparison with the performance evaluation of the past and contribute to the accumulation of data in the future.
In addition, as a result of conducting various studies, the present inventors took note of the fact that an xe2x80x9coptimization design techniquexe2x80x9d which is being used in different fields is applicable to the special field of tires, and conducted studies from various angles, and specifically established this technique specifically as a method of designing a tire, so as to estimate tire performance in the optimization process, i.e., to estimate the performance of an actually used tire in the presence of a fluid, such as the drainage performance, in-snow performance, and noise performance, to bring the fluid during the ground contacting and rolling of the tire close to a flowing state and enable transient analysis, to make efficient the development of the tire, and to facilitate the provision of the tire having excellent performance.
Specifically, the method of designing a pneumatic tire according to claim 28 of the invention comprises the steps of: (11) determining a tire model which includes at least a cross-sectional shape of a tire including an internal structure and which has a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, determining a fluid model which is partially or wholly filled with a fluid and which comes into contact with at least a portion of the tire model, determining an objective function representing a physical quantity for evaluating tire performance, a design variable for determining a cross-sectional shape of the tire, a tire structure, or a pattern configuration, and determining a constraint for constraining at least one of the cross-sectional shape of the tire, the tire structure, the pattern configuration, the physical quantity for evaluating performance, and a tire size; (12) estimating the tire performance on the basis of the physical quantity occurring in at least one of the tire model and the fluid model in at least one of a state of deformation of the tire model and a state of pseudo flow of the fluid model; (13) determining a value of the design variable which gives an optimum value of the objective function while satisfying the estimated tire performance and the constraint; and (14) designing the tire on the basis of the design variable which gives the optimum value of the objective function.
In accordance with the invention according to claim 29, in the method of designing a pneumatic tire according to claim 28, wherein step (12) includes the steps of: (15) executing a deformation calculation of the tire model; (16) executing a fluid calculation of the fluid model; (17) identifying a boundary surface between the tire model after the deformation calculation in step (15) and the fluid model after the fluid calculation in step (16), imparting a boundary condition concerning the identified boundary surface to the tire model and the fluid model, and performing the calculations until the fluid model assumes a state of pseudo flow; (18) determining a physical quantity occurring in at least one of the tire model and the fluid model in step (15) or step (16); and (19) estimating the tire performance on the basis of the physical quantity.
In accordance with the invention according to claim 30, in the method of designing a pneumatic tire according to claim 28 or 29, in step (11), a road surface model in contact with the fluid model is further determined.
In accordance with the invention according to claim 31, in the method of designing a pneumatic tire according to claim 29 or 30, in step (15), the deformation calculation is performed repeatedly for only a predetermined time duration.
In accordance with the invention according to claim 32, in the method of designing a pneumatic tire according to any one of claims 29 to 31, wherein, in step (16), the fluid calculation is performed repeatedly for only a fixed time duration.
In accordance with the invention according to claim 33, in the method of designing a pneumatic tire according to any one of claims 29 to 32, in step (17), the deformation calculation and fluid calculation are performed repeatedly for only a time duration determined in advance.
In accordance with the invention according to claim 34, in the method of designing a pneumatic tire according to any one of claims 28 to 33, in a case where the tire model is rolled, in step (11), the tire model is determined for which the calculations for a time of charging with internal pressure and a time of load calculation is performed, and to which a rotational displacement or a speed or a straightly advancing displacement or speed is imparted.
In accordance with the invention according to claim 35, in the method of designing a pneumatic tire according to any one of claims 28 to 34, in a case where the tire model is rolled, in step (11), influx and efflux conditions representing that the fluid flows out freely from a top surface of the fluid model and that the fluid does not flow into or flow out of surfaces other than the top surface of the fluid model are imparted to the fluid model.
In accordance with the invention according to claim 36, in the method of designing a pneumatic tire according to any one of claims 28 to 35, wherein in a case where the tire model is not rolled, in step (11), the tire model is determined for which the calculations for charging with internal pressure are performed, and for which load calculation is performed after the calculations.
In accordance with the invention according to claim 37, in the method of designing a pneumatic tire according to any one of claims 28 to 34 or claim 36, wherein in a case where the tire model is not rolled, in step (11), influx and efflux conditions representing that the fluid flows into a front surface of the fluid model at an advancing velocity, that the fluid flows out freely from a rear surface of the fluid model and a top surface of the fluid model, and that the fluid does not flow into or flow out of side surfaces of the fluid model and a lower surface of the fluid model are imparted to the fluid model.
In accordance with the invention according to claim 38, in the method of designing a pneumatic tire according to any one of claims 28 to 37, the tire model has a pattern partially.
In accordance with the invention according to claim 39, in the method of designing a pneumatic tire according to any one of claims 28 to 38, wherein, as for the road surface model, a road surface condition is set by selecting a coefficient of friction xcexc representing at least one of road surface conditions including dry, wet, icy, snowy, and unpaved conditions.
In accordance with the invention according to claim 40, in the method of designing a pneumatic tire according to any one of claims 28 to 39, wherein, in step (17), an interfering portion between the tire model and the fluid model is generated, the interference portion is identified, and the fluid model is divided by fluid elements with a surface of the tire model as a boundary surface.
In accordance with the invention according to claim 41, in the method of designing a pneumatic tire according to any one of claims 28 to 40, the fluid model contains at least water, at least one of a ground contact area and a ground contact pressure of the tire model is used as the physical quantity, and a wet performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 42, in the method of designing a pneumatic tire according to any one of claims 28 to 41, wherein the fluid model contains at least water, at least one of a pressure, flow volume, and flow velocity of the fluid model is used as the physical quantity, and a wet performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 43, in the method of designing a pneumatic tire according to any one of claims 28 to 42, wherein the fluid model contains at least one of water and snow, at least one of a ground contact area, ground contact pressure, and shearing force of the tire model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, and an on-ice and in-snow performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 44, in the method of designing a pneumatic tire according to any one of claims 28 to 43, wherein the fluid model contains at least one of water and snow, at least one of a pressure, flow volume, and flow velocity of the fluid model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, and an on-ice and in-snow performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 45, in the method of designing a pneumatic tire according to any one of claims 28 to 44, the fluid model contains at least water, at least one of a pressure, flow volume, flow velocity, energy, and energy density of the fluid model is used as the physical quantity, and a noise performance of the tire is estimated as the tire performance.
In accordance with the invention according to claim 47, in the method of designing a pneumatic tire according to claim 28, the design variable includes at least one of: a function representing a shape of at least one line selected from a carcass line, a turn-up ply line, a line representing an outer configuration of the tire, a line representing a tire crown shape, and a reinforcing-material line; a variable representing at least one gauge distribution of a tire rubber member selected from a gauge distribution of a bead filler, a gauge distribution of a rubber chafer, a gauge distribution of side rubber, a gauge distribution of tread rubber, a gauge distribution of tread base rubber, a gauge distribution of inner-surface reinforcing rubber, a gauge distribution of inter-belt rubber, and a gauge distribution of belt end rubber; a variable representing at least one structure of a belt portion selected from an angle of each belt layer, a width thereof, a cord type thereof, and a placing density thereof; and a variable representing at least one configuration of a pattern selected from a configuration of a block, a position of a sipe, a number of sipes, and a length of each of the sipes.
In the present invention, first, a draft design of the tire is incorporated into a model in numerical analysis so as to estimate the performance of a tire to be evaluated (such as the change of the shape, structure, materials, and pattern of the tire). Further, modeling of a fluid and a road surface concerning the targeted performance is performed to construct a fluid model and a road surface model (numerical analysis models), numerical analysis which simultaneously takes into consideration the tire, the fluid, and the road surface is carried out, and the targeted performance is numerically estimated. The acceptability of the draft design of the tire can be determined from the result of this estimation, and if the result is favorable, the draft design is adopted, or a further improvement of the evaluation of the performance of this draft design becomes possible. If these procedures are used, the number of times the tire is manufactured and the performance is evaluated can be minimized, so that the development of the tire can be made efficient.
Accordingly, to undertake the development of the tire based on the estimation of performance, numerical analysis models for the tire performance estimation which is efficient and highly accurate are essential. Accordingly, to estimate the tire performance, in step (11), a tire model which includes at least a cross-sectional shape of the tire including an internal structure and which has a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling, as well as a fluid model which is filled with a fluid at least partially and comes into contact with at least a portion of the tire model, are determined. Incidentally, a road surface model may be further determined.
In addition, in step (11), the objective function representing the physical quantity for evaluating tire performance, the design variable for determining the cross-sectional shape of the tire or the tire structure, and the constraint for constraining the cross-sectional shape of the tire or the tire structure are determined. In addition to a line representing the outer configuration of the tire, this tire model may include a line representing the configuration of a tire crown, a belt line representing a belt in the interior of the tire, a carcass line representing the carcass of the tire, a turn-up ply line representing a turn-up line of the carcass ply in the interior of the tire, and a reinforcing-material line representing a line of each of various reinforcing materials, the gauge distribution of a tire rubber member, the angle, width, cord type, and placement density of each belt layer representing the structure of the belt portion, as well as the configuration of a block, the block groove-wall angle, the position of a sipe, the number of sipes, and the length of the sipe which represent the configuration of the pattern.
In addition, a technique called the finite element method for dividing the tire model into a plurality of elements or an analytical technique may be used for the tire model. As the objective function representing a physical quantity for evaluating tire performance, it is possible to use a physical quantity for governing the relative excellence of the tire performance, including the lateral spring constant and belt tension in the circumferential direction of the tire when inflated with tire to improve steering stability. As the design variable, it is possible to use, among others, a function representing at least one line selected from the carcass line, the turn-up ply line, the outer configuration of the tire, the line representing the configuration of the tire crown, and the reinforcing-material line representing the line of each reinforcing material. As the design variable for determining the tire structure, it is possible to use a variable representing at least one gauge distribution of a tire rubber member selected from a gauge distribution of a bead filler, a gauge distribution of a rubber chafer, a gauge distribution of side rubber, a gauge distribution of tread rubber, a gauge distribution of tread base rubber, a gauge distribution of inner-surface reinforcing rubber, a gauge distribution of inter-belt rubber, and a gauge distribution of belt end rubber, as well as a variable representing the structure of the belt portion, the bead and side portions, including an angle of a belt layer, the width of the belt layer, the height of the ply, an amount of the ply turned up, and the angle, width, position, material and the like of a bead-portion reinforcing material.
In addition, as the design variable for determining the pattern, it is possible to use a variable representing the configuration of the pattern, including the configuration of a block, the block groove-wall angle, the position of a sipe, the number of sipes, and the length of the sipe. As the constraint for constraining the cross-sectional configuration of the tire and the tire structure, it is possible to cite, for example, a constraint in a periphery value of the carcass line, a constraint in the vertical primary eigenfrequency, a constraint in the angle of the belt layer, a constraint in the width of the belt layer, and constraints such as the tire size, spring constants, the amount of deformation of the tire, tire weight, stress, strain, strain energy, and rolling resistance. It should be noted that the objective function, the design variable, and the constraint are not confined to the aforementioned examples, and various items may be set as such depending on the objective of tire design.
Next, in step (12), the tire performance is estimated on the basis of the physical quantity occurring in at least one of the tire model and the fluid model in at least one of a state of deformation of the tire model and a state of pseudo flow of the fluid model. In this step (12), deformation calculation of the tire model is executed in step (15), and fluid calculation of the fluid model is executed in step (16). In step (17), a boundary surface between the tire model after the deformation calculation in step (15) and the fluid model after the fluid calculation in step (16) is recognized, a boundary condition concerning the recognized boundary surface is imparted to the tire model and the fluid model, and the calculation is performed until the fluid model assumes a state of pseudo flow. In step (18), a physical quantity occurring in at least one of the tire model and the fluid model in step (15) or step (16) is determined and, in step (19), the tire performance can be estimated on the basis of the physical quantity.
In the deformation calculation of the tire model in step (15), deformation calculation at a time when deformation is imparted by at least one of ground contacting and rolling can be executed. In this case, at least one of the ground contacting and rolling may be set as the input.
In addition, when a boundary condition concerning the recognized boundary surface is imparted to the tire model and the fluid model, the fluid model may be determined in such a manner that the fluid is present on the road surface model side relative to the boundary surface.
It should be noted that, in at least one of the deformation calculation of the tire model and fluid calculation, repeated calculation may be performed. In the deformation calculation of the tire model, 10 msec or less may be adopted as the elapsed time of the predetermined time duration during which the repeated calculation is performed. Preferably, it is possible to adopt 1 msec or less, more preferably 1xcexcxc2x7sec or less. In addition, in the fluid calculation, 10 msec or less may be adopted as the elapsed time of the fixed time duration during which the repeated calculation is performed. Preferably, it is possible to adopt 1 msec or less, more preferably 1xcexcxc2x7sec or less. If this elapsed time is too long, the fluid in the fluid model fails to assume a state of pseudo flow conforming to the behavior of the tire, and the accuracy as a numerical model deteriorates. For this reason, it is necessary to adopt an appropriate value as the elapsed time.
In addition, repeated calculation may be performed also in the calculation until the fluid model assumes the state of pseudo flow. In this calculation, 10 msec or less may be adopted as the elapsed time of the predetermined time duration during which the repeated calculation is performed. Preferably, it is possible to adopt 1 msec or less, more preferably 1xcexcxc2x7sec or less.
The aforementioned tire model may have a pattern partially. Further, as for the road surface model, an actual road surface condition can be reproduced by selecting a coefficient of friction xcexc representing a road surface condition among the dry, wet, icy, snowy, unpaved and other conditions depending on the road surface condition.
When the boundary condition is imparted, it is important that the fluid model recognize the surface of the tire model as the boundary surface of the fluid. However, if the very fine elements making up the fluid model are always made sufficiently small with respect to the tire (particularly pattern) model, and the number of constituent elements of the fluid model hence increases, an increase in the calculation time results, which entails difficulty. Accordingly, it is preferable to prevent an increase in the calculation time by making the very fine elements making up the fluid model large to a certain measure. At the same time, it is preferable to produce (overlap) an interfering portion between the tire model and the fluid model, recognize the interference portion, and divide the fluid model with the surface of the tire model as a boundary surface, so as to allow the boundary surface between the tire model and the fluid model to be recognized with high accuracy.
In addition, if the fluid model contains at least water, and the ground contact area or ground contact pressure of the tire model is used as the physical quantity, it is possible to estimate the wet performance of the tire. Further, if the fluid model contains at least water, and the pressure, flow volume, or flow velocity of the fluid model is used as the physical quantity, it is possible to estimate the wet performance of the tire.
Further, if the fluid model contains at least one of water and snow, and at least one of the ground contact area, ground contact pressure, and shearing force of the tire model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, it is possible to estimate the on-ice and in-snow performance of the tire. In addition, if the fluid model contains at least one of water and snow, and at least one of the pressure, flow volume, and flow velocity of the fluid model on at least one of an icy road surface and a snowy road surface is used as the physical quantity, it is possible to estimate the on-ice and in-snow performance of the tire.
Further, if the fluid model contains at least water, and at least one of the pressure, flow volume, flow velocity, energy, and energy density of the fluid model is used as the physical quantity, it is possible to estimate the noise performance of the tire.
Next, in step (13), the value of the design variable which gives an optimum value of the objective function while taking the estimated tire performance and the constraint into consideration is determined. In this case, it is effective if an amount of change of the design variable which gives the optimum value of the objective function while taking the constraint into consideration is estimated on the basis of a sensitivity of the objective function, which is a ratio of an amount of change of the objective function to an amount of unit change of the design variable, and a sensitivity of the constraint, which is a ratio of an amount of change of the constraint to an amount of unit change of the design variable, a value of the objective function when the design variable is changed by an amount corresponding to the estimated amount and a value of the constraint when the design variable is changed by the amount corresponding to the estimated amount are calculated, and the value of the design variable which gives the optimum value of the objective function while taking the constraint into consideration is determined on the basis of the estimated value and the calculated values. By so doing, it is possible to obtain the value of the design variable which gives an optimum value of the objective function while taking the constraint into consideration.
In addition, as a result of conducting various studies, the present inventors took note of the fact that the xe2x80x9ctechnique of genetic algorithmsxe2x80x9d which is being used in different fields is applicable to the special field of tires, and conducted studies from various angles, and specifically established this technique specifically as a method of designing a tire, so as to estimate tire performance in the process of the genetic algorithm, i.e., to estimate the performance of an actually used tire in the presence of a fluid, such as the drainage performance, in-snow performance, and noise performance, to bring the fluid during the ground contacting and rolling of the tire close to a flowing state and enable transient analysis, to make efficient the development of the tire, and to facilitate the provision of the tire having excellent performance.
Specifically, in accordance with the invention according to claim 48, in the method of designing a pneumatic tire according to claim 28, step (11) comprises: determining a group subject to selection, including a plurality of tire models each of which includes at least a cross-sectional shape of the tire including an internal structure and has a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling; and determining, with respect to each of the tire models of the group subject to selection, the objective function representing the physical quantity for evaluating the tire performance, the design variable for determining the cross-sectional shape of the tire or the tire structure or a pattern configuration, the constraint for constraining at least one of the cross-sectional shape of the tire, the tire structure, the pattern configuration, the physical quantity for evaluating performance, and the tire size, and an adaptive function which can be evaluated from the objective function and the constraint; and step (13) comprises: selecting two tire models from the group subject to selection on the basis of the adaptive function; effecting at least one of generating a new tire model by allowing design variables of the tire models to cross over each other at a predetermined probability and generating a new tire model by changing a portion of the design variable of at least one of the tire models; determining the objective function, the constraint, and the adaptive function of the new tire model with the design variable changed; preserving said new tire model and one of the plurality of tire models with the design variable not changed, the processing being repeated until the tire models preserved reach a predetermined number; determining whether or not a new group including the predetermined number of the preserved tire models satisfies the predetermined convergence criterion; if the convergence criterion is not satisfied, repeating the processing until the group subject to selection satisfies the predetermined convergence criterion by setting the new group as the group subject to selection; and if the predetermined convergence criterion is satisfied, determining a value of the design variable which gives an optimum value of the objective function among the predetermined number of the preserved tire models while satisfying the constraint.
In accordance with the invention according to claim 49, in the method of designing a pneumatic tire according to claim 48, in step (13), with respect to the tire model with the design variable changed, an amount of change of the design variable which gives the optimum value of the objective function is estimated while satisfying the constraint on the basis of the sensitivity of the objective function, which is a ratio of an amount of change of the objective function to an amount of unit change of the design variable, and on the basis of the sensitivity of the constraint, which is a ratio of an amount of change of the constraint to an amount of unit change of the design variable, a value of the objective function when the design variable is changed by an amount corresponding to the estimated amount and a value of the constraint when the design variable is changed by an amount corresponding to the estimated amount are calculated, an adaptive function is determined from the value of the objective function and the value of the constraint, said new tire model and the one of the plurality of tire models with the design variable not changed are preserved, and the processing is repeated until the preserved basic models of the tire reach the predetermined number.
In the invention according to claim 48, it is effective if step (11) comprises: determining a group subject to selection, consisting of a plurality of tire models which each includes at least a cross-sectional shape of the tire including an internal structure and which has a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling; and determining, with respect to each of the tire models of the group subject to selection, the objective function representing the physical quantity for evaluating tire performance, the design variable for determining the cross-sectional shape of the tire or the tire structure, the constraint for constraining at least one of the cross-sectional shape of the tire, the tire structure, the pattern configuration, the physical quantity for evaluating performance, and the tire size, and an adaptive function which can be evaluated from the objective function and the constraint; and step (13) comprises: selecting two tire models from the group subject to selection on the basis of the adaptive function; effecting at least one of generating a new tire model by allowing design variables of the tire models to cross over each other at a predetermined probability and generating a new tire model by changing a portion of the design variable of at least one of the tire models; determining the objective function, the constraint, and the adaptive function of the tire model with the design variable changed; preserving the tire model and the tire model with the design variable not changed, the processing being repeated until the tire models preserved reaches a predetermined number; determining whether or not a new group consisting of the predetermined number of the preserved tire models satisfies a predetermined convergence criterion; if the convergence criterion is not satisfied, repeating the processing until the group subject to selection satisfies a predetermined convergence criterion by setting the new group as the group subject to selection; and if the predetermined convergence criterion is satisfied, determining the value of the design variable which gives the optimum value of the objective function among the predetermined number of the preserved tire models while taking the constraint into consideration.
In this case, it is effective if, in step (13), with respect to the tire model with the design variable changed, the amount of change of the design variable which gives the optimum value of the objective function is estimated while taking the constraint into consideration on the basis of the sensitivity of the objective function, which is the ratio of the amount of change of the objective function to the amount of unit change of the design variable, and on the basis of the sensitivity of the constraint, which is the ratio of the amount of change of the constraint to the amount of unit change of the design variable, the value of the objective function when the design variable is changed by the amount corresponding to the estimated amount and the value of the constraint when the design variable is changed by the amount corresponding to the estimated amount are calculated, the adaptive function is determined from the value of the objective function and the value of the constraint, the tire model and the tire model with the design variable not changed are preserved, and the processing is repeated until the preserved basic models of the tire reaches the predetermined number. By so doing, it is also possible to obtain the value of the design variable which gives an optimum value of the objective function while taking the constraint into consideration. It should be noted that as for the adaptive function which can be evaluated from the objective function and the constraint, it is possible to use a function for determining the fitness with respect to the tire model from the objective function and the constraint. Further, the objective function, the design variable, the constraint, and the adaptive function are not confined to the aforementioned examples, and various items may be set as such depending on the objective of tire design. Further, in the crossover of the design variables of the basic models of the tire, there is a method wherein a part of the design variable or design variables at or subsequent to a predetermined position are exchanged with respect to the design variables of two tire models selected. Furthermore, in the change of a part of the design variable of the tire model, there is a method wherein the design variable at a position determined at a predetermined probability is changed (mutated).
In addition, as a result of conducting various studies, the present inventors took note of the fact that a xe2x80x9cnonlinear prediction technique in which a neuro circuit network of the higher animal is modeled in engineering, e.g., a neural network,xe2x80x9d and the xe2x80x9coptimization design techniquexe2x80x9d which are being used in different fields are applicable to the special field of tires, and conducted studies, and specifically established these techniques specifically as a method of designing a tire.
Specifically, in accordance with the invention according to claim 50, in the method of designing a pneumatic tire according to claim 28, in step (11), a transformation system is determined in which nonlinear correspondence is correlated between a design parameter of the tire which includes at least the cross-sectional shape of the tire including the internal structure and which has the pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling on the one hand, and the performance of said tire on the other hand, and a constraint for constraining an allowable range of at least one of the tire performance and a manufacturing condition of the tire is determined as the constraint; in step (13), the design parameter of the tire which gives the optimum value of the objective function on the basis of the objective function and the constraint is determined by using the transformation system determined in step (11); and in step (14), the tire is designed on the basis of the design parameter of the tire.
In accordance wit h the invention according to claim 51, in the method of designing a pneumatic tire according to claim 50, in step (13), the design parameter of the tire is set as the design variable, and the value of the design variable which gives the optimum value of the objective function is determined by using the transformation system determined in step (11) while satisfying the constraint; and in step (14), the tire is designed on the basis of the design variable which gives the optimum value of the objective function.
In accordance with the invention according to claim 52, in the method of designing a pneumatic tire according to claim 50 or 51, transformation system is formed by data of a multilayered feedforward-type neural network which has undergone learning so as to transform the design parameter of the tire into the tire performance.
The tire performance, e.g., the values of the steering stability and belt durability and the like, are determined by the design parameters of the tire design, e.g., the cross-sectional configuration of the tire including the internal structure and the tire structure. However, there are many cases where even if the values of the cross-sectional configuration of the tire and the tire structure are varied linearly, the tire performance does not change linearly. Accordingly, in step (11) of the invention, a transformation system is determined in which nonlinear correspondence is correlated between a design parameter of the tire which includes at least a cross-sectional shape of the tire including an internal structure and which has a pattern configuration to which deformation can be imparted by at least one of ground contacting and rolling on the one hand, and the performance of the tire on the other hand. In addition, a constraint for constraining an allowable range of at least one of the tire performance and a manufacturing condition of the tire is determined as the constraint. This transformation system can be determined by using a nonlinear prediction technique in which a neuro circuit network of the higher animal is modeled in engineering, such as a neural network. In addition, as the objective function representing a physical quantity for evaluating tire performance, it is possible to use a physical quantity for governing the relative excellence of the tire performance including the lateral spring constant and belt tension in the circumferential direction of the tire when inflated with tire to improve steering stability, or the ground contacting characteristic within the ground contact plane during straightly advancing or lateral force. As the constraint for constraining an allowable range of at least one of the tire performance and the design parameter of the tire, e.g., as the constraint for constraining the cross-sectional configuration of the tire and the tire structure, it is possible to cite, for example, a constraint in a periphery value of the carcass line, a constraint in the vertical primary eigenfrequency, a constraint in the angle of the belt layer, a constraint in the width of the belt layer, and constraints such as the tire size, spring constants, the amount of deformation of the tire, tire weight, stress, strain, strain energy, and rolling resistance. It should be noted that the objective function and the constraint are not confined to the aforementioned examples, and various ones items may be set as such depending on the objective of tire design.
In step (13), the design parameter of the tire which gives the optimum value of the objective function on the basis of the objective function and the constraint is determined by using the transformation system determined in step (11); and in step (14), the tire is designed on the basis of the design parameter of the tire. As a result, a transformation system is determined in which nonlinear correspondence is correlated between the design parameter of the tire and the tire performance, and it is possible to ascertain a mutual relationship of correspondence in which design parameters of the tire and their performances are correlated. Hence, the design of a high-performance tire becomes possible by designing the tire on the basis of the design parameters by determining the design parameters of the tire which give optimum values of the objective function.
In the case where the tire is designed, the design parameter of the tire can be set as the design variable, and the value of the design variable which gives the optimum value of the objective function can be determined by using the transformation system determined in step (11) while taking the constraint into consideration, making it possible to design the tire on the basis of the design variable which gives the optimum value of the objective function. Thus, by taking the constraint into consideration, it is possible to take into consideration the allowable range of at least one of the tire performance and the design parameter of the tire, and it is possible to specify the design range in advance or set a desired range.
In addition, in a case where the value of the design variable is determined, it is effective if an amount of change of the design variable which gives the optimum value of the objective function while taking the constraint into consideration is estimated on the basis of a sensitivity of the objective function, which is a ratio of an amount of change of the objective function to an amount of unit change of the design variable, and a sensitivity of the constraint, which is a ratio of an amount of change of the constraint to an amount of unit change of the design variable, a value of the objective function when the design variable is changed by an amount corresponding to the estimated amount and a value of the constraint when the design variable is changed by the amount corresponding to the estimated amount are calculated, and the value of the design variable which gives the optimum value of the objective function while taking the constraint into consideration is determined on the basis of the estimated value and the calculated values by using the transformation system determined in Step (11). By so doing, it is possible to obtain the value of the design variable which gives an optimum value of the objective function while taking the constraint into consideration. Then, the tire can be designed by changing the design parameter and the like of the tire on the basis of the design variable which gives the optimum value of the objective function.
Still further, in the present invention, by designing a tire in which the block height within each block which is present in the tread pattern is uniquely optimized in correspondence with ground contact pressure for the input to which the tire is subjected, nonuniformity of the ground contact pressure within the tire pattern or within the block is corrected. Namely, in the case of the tread configuration in which the block height is set to a fixed level, the ground-contact-pressure distribution characteristic becomes nonuniform within the block. In the present invention, by changing the tread configuration, it is possible to obtain a ground-contact-pressure distribution characteristic which becomes substantially uniform within the block.
For this reason, in the present invention, a basic model of the configuration is first constructed, and an input condition is imparted thereto. The value of the objective function is calculated from the ground contact pressure determined at this juncture. Then, the design variable is set as the tread configuration of the block, a change of the configuration is made, an input is imparted again to the model using this new configuration, and the distribution of the ground contact pressure is obtained. This operation is repeated until an optimum value of the objective function is given. It should be noted that the present invention is applicable to a case where the constraint is provided, in which case the value of the objective function and the value of the constraint are obtained after imparting an input to the basic model. The design in this case ends when an optimum value of the objective function is obtained within the constraint. The tire is designed on the basis of this optimum design variable.
Specifically, in accordance with the invention according to claim 53, in the method of designing a pneumatic tire according to claim 28, in step (11), a basic model of a configuration representing one configuration selected from a configuration of a unit body of a block including an internal structure, a partial pattern configuration of a tire crown portion including the internal structure, and a configuration of a land portion continuing in a circumferential direction of the tire and including the internal structure is further determined; at least one input condition is imparted to the basic model of the configuration; a tread configuration representing at least one portion of the configuration of the unit body of the block, the pattern configuration, or the configuration of the land portion is set as the design variable; and a ground contact pressure of the tire under the input condition is calculated and set as the objective function.
In accordance with the invention according to claim 54, in the method of designing a pneumatic tire according to claim 53, at least one of a tire contact area and a range of change of the design variable is further set as the constraint, and, in step (13), the value of the design variable is changed until an optimum value of the objective function is given while satisfying the constraint.
In accordance with the invention according to claim 55, in the method of designing a pneumatic tire according to claim 54, as for the design variable, the design variable for at least one of a location where the ground contact pressure is higher than average ground contact pressure and a location where the ground contact pressure is lower than average ground contact pressure is changed.
The basic model of the configuration represents one configuration selected from the configuration of a unit body of a block including an internal structure, a partial pattern configuration of a tire crown portion including the internal structure, and the configuration of a land portion continuing in the circumferential direction of the tire and including the internal structure.
The basic model of the configuration representing the configuration of a unit body of a block may be constituted by a function representing a line for specifying the outer configuration of the unit body of the block or a variable representing the coordinate values of an inflection point. In addition, the basic model of the configuration representing the partial pattern configuration of the tire crown portion including the internal structure may be constituted by a function which is capable of geometrically analyzing the pattern configuration on the ground-surface contacting side of one land portion among the tire crown portions, e.g., a function for determining a polygon such as a rectangle or a rhombus. In addition, the basic model of the configuration representing the configuration of a land portion continuing in the circumferential direction of the tire and including the internal structure may be constituted by a function representing a line representing the cross-sectional configuration of the tire or a variable representing the coordinate values of an inflection point. As these basic models of the configuration, it is possible to use a model based on the technique called the finite element method for dividing the model into a plurality of elements or a model based on an analytical method.
In addition, at least one input condition is imparted to the basic model of the configuration. The input conditions include a load condition representing the load to be applied and a direction condition representing the shearing direction. Next, the tread configuration representing at least a portion of the shape of the unit body of the block, the pattern configuration, or the configuration of the land portion is set as the design variable, and the ground contact pressure of the tire is calculated under the input condition and is set as the objective function.
In addition, in step (13), it is possible to determine the value of the design variable which gives an optimum value of the objective function, and it is possible to determine the value of the design variable by calculating the value of the design variable while changing the value of the design variable until the optimum value of the objective function is given.
When the tread configuration is set as the design variable, and the ground contact pressure of the tire is calculated under the input condition and is set as the objective function, it is preferable to take the constraint into consideration to alleviate the calculational load and the like. Accordingly, at least one of the tire contact area and a range of change of the design variable is further set as the constraint, and, in step (13), the value of the design variable is changed until an optimum value of the objective function is given while taking the constraint into consideration. This range of change of the design variable can be represented by either the range of the tread or the block height.
When the value of the design variable which gives the optimum value of the objective function is determined, the design variable for at least one of a location where the ground contact pressure is higher than average ground contact pressure of the tire and a location where the ground contact pressure is lower than average ground contact pressure of the tire can be changed. In a case where the design variable for a location where the ground contact pressure is higher than average ground contact pressure of the tire is thus changed, the design variable can be changed in such a manner as to decrease the block height. Meanwhile, in a case where the design variable for a location where the ground contact pressure is lower than average ground contact pressure of the tire is changed, the design variable can be changed in such a manner as to increase the block height. Further, the design variable can be changed by changing the block height in correspondence with each deviation from the average ground contact pressure of the tire.
It should be noted that in a case where there are a plurality of input conditions, the design variable may be changed by placing priority on an input condition whose amount of change of the block height is larger.
In addition, the at least one portion of the tread configuration represented by the design variable can be represented by a mathematical formula of any one of a polynomial, a division polynomial, a spline function, and a rational function. In a case where at least one portion of the tread configuration represented by such a mathematical formula is changed, the change may be effected for each calculation or once for a number of calculations by taking into account the calculation time and the capacity of the computer.
It should be noted that, by forming the tire by the structure and the like using the design parameters of the tire designed by the above-described method of designing a tire, the performance of the tire thus formed is designed with optimum design parameters, so that it is possible to directly determine the details of optimum design parameters depending on the conditions of application such as the manufacturing conditions and cost.
It should be noted that if the tire designed by the above-described method of designing a pneumatic tire is manufactured, it is possible to obtain a tire exhibiting satisfactory tire performance. Accordingly, in the present invention, it is possible to design the vulcanizing mold for a tire and manufacture the tire in the manner described below.
In the method of designing a vulcanizing mold for a tire in accordance with the invention according to claim 56, a vulcanizing mold for a tire is designed on the basis of the tire or the tire model designed by the method of designing a pneumatic tire according to any one of claims 28 to 55.
In the method of make a vulcanizing mold for a tire in accordance with the invention according to claim 57, a vulcanizing mold for a tire designed by the method of designing a vulcanizing mold for a tire according to claim 56 is made.
In the method of manufacturing a pneumatic tire in accordance with the invention according to claim 58, a vulcanizing mold for a tire designed by the method of designing a vulcanizing mold for a tire according to claim 56 is made, and a pneumatic tire is manufactured by using the vulcanizing mold.
In the method of designing a pneumatic tire in accordance with the invention according to claim 59, a pneumatic tire is manufactured on the basis of the tire or the tire model designed by the method of designing a pneumatic tire according to any one of claims 28 to 55.
Namely, in the case where the vulcanizing mold for a tire for manufacturing a tire is designed, the vulcanizing mold for a tire is designed on the basis of the tire or the tire model designed by the method of designing a pneumatic tire according to any one of claims 28 to 55. Since the tire performance is estimated in this manner, and the vulcanizing mold for a tire is designed on the basis of the tire model having that tire performance, it is possible to evaluate the flow of the fluid around the tire to be manufactured, and estimate the smoothness of flow and the occurrence of disturbance, thereby making it possible to contribute to the design of the mold for manufacturing a tire while estimating the tire performance.
If the vulcanizing mold for a tire thus designed is made, the manufacture of the tire to be provided with the estimated tire performance is facilitated. In addition, if this vulcanizing mold for a tire is made, and the tire is manufactured by using the same, its tire performance substantially agrees with the estimated performance, and it is possible to obtain a tire in which the evaluation of the flow of the fluid, the smoothness of the flow, the occurrence of disturbance, and the like have been taken into consideration.
In addition, in the case where the tire is manufactured, the vulcanizing mold for a tire designed by the method of designing a vulcanizing mold for a tire according to claim 56 is made, and the pneumatic tire is manufactured by using that vulcanizing mold. Alternatively, if the pneumatic tire is manufactured on the basis of the tire or the tire model designed by the method of designing a pneumatic tire according to any one of claims 28 to 55, as described in claim 59, its tire performance substantially agrees with the estimated performance, and it is possible to obtain a tire in which the evaluation of the flow of the fluid, the smoothness of the flow, the occurrence of disturbance, and the like have been taken into consideration.
As also described in claim 60, the above-described method of designing a tire can be realized by an optimization analyzer comprising: estimating means for estimating the performance of a tire from a design parameter of the tire; transformation-system computing means for determining a nonlinear relationship of correspondence between the design parameter of the tire and the performance of the tire; input means for determining an objective function representing the tire performance, determining a constraint for constraining an allowable range of at least one of the tire performance and a manufacturing condition of the tire, and inputting them as items of optimization; and optimization calculating means for determining the design parameter of the tire which gives the optimum value of the objective function on the basis of the items of optimization inputted by the input means by using the transformation-system computing means.
As also described in claim 61, this transformation-system computing means is able to determine a nonlinear relationship of correspondence between the design parameter of the tire and an applicable condition for the tire on the one hand, and the performance of the tire on the other hand. The applicable conditions include the constituent members of the tire, their volumes and sizes, the manufacturing conditions, the weight of the tire, and overall cost. In addition, the transformation-system computing means may be constituted by a multilayered feedforward-type neural network which has undergone learning so as to transform the design parameter of the tire into the tire performance.
As also described in claim 62, the above-described method of designing a tire is able to provide a recording medium on which a tire optimization analysis program recorded thereon and which can be easily carried around by virtue of the recording medium containing a program based on the following procedures: Namely, this recording medium is a recording medium with a tire optimization analysis program recorded thereon for designing a tire by a computer, wherein the optimization analysis program is arranged to: estimate the performance of a tire from a design parameter of the tire; determine a nonlinear relationship of correspondence between the design parameter of the tire and the performance of the tire; determine an objective function representing the tire performance, determine a constraint for constraining an allowable range of at least one of the tire performance and a manufacturing condition of the tire; and determine the design parameter of the tire which gives the optimum value of the objective function on the basis of the determined relationship of correspondence, the objective function, and the constraint, and design the tire on the basis of the design parameter of the tire.
As described above, in accordance with the present invention, an advantage is offered in that it is possible to obtain a tire which is capable of estimating tire performance in an environment of actual use in the presence of a fluid, such as the drainage performance, in-snow performance, and noise performance, which is capable of enabling analysis in which the fluid during the ground contacting and rolling of the tire is taken into consideration, and which is capable of improving the efficiency in tire development and has excellent performance.
In addition, an advantage is offered in that it is possible to obtain a tire which is capable of determining a design variable which gives an optimum value of the objective function satisfying the constraint while estimating tire performance in the environment of actual use in the presence of a fluid, such as the drainage performance, in-snow performance, and noise performance, and of designing a tire on the basis of this design variable, which is capable of enabling analysis in which the fluid during the ground contacting and rolling of the tire is taken into consideration, and which makes it possible to improve the efficiency in tire development and has excellent performance.